arXiv:2609.06182v1 Announce Type: cross
Abstract: In this paper, we develop and analyze techniques for recovering a linear image $Bx$ of an unknown signal $x$ from indirect noisy observation $\omega=...
By Anatoli Juditsky, Arkadi Nemirovski
The paper introduces a transfer learning framework for structured matrix estimation when both the ambient dimension and the intrinsic representation grow over time. It models the target parameter as an embedded source component plus low‑rank innovations and sparse edits, and proposes an anchored alternating projection estimator that preserves the transferred subspace while estimating only the new components. Deterministic error bounds are derived that separate target noise, representation growth, and source estimation error, showing improved rates when rank and sparsity increments are small, and the framework is applied to Markov transition matrix estimation and structured covariance estimation with theoretical guarantees and empirical validation.
By Jinhang Chai, Xuyuan Liu, Elynn Chen, Yujun Yan
The paper introduces a structured method for learning linear operators in control systems using data. It leverages the framework of (semi)groups for evolution equations to establish structural assumptions and applies inverse‑problems theory to analyze learning algorithms, revealing error decompositions, convergence guarantees, and optimal regularization. Focusing on bounded operators on Hilbert spaces, the authors derive a convergent estimator for time‑varying systems, illustrating the practical power of their approach.
By Max Beier, Nicolas Hoischen, Sandra Hirche, Petar Bevanda
arXiv:2609.09211v1 Announce Type: new
Abstract: The Davis-Kahan theorem is a fundamental tool in spectral analysis, providing quantitative control over the distance between the eigenspaces of a symme...
By Huan Qing
arXiv:2607. 07468v1 Announce Type: cross Abstract: We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning.
By Abhishake Rastogi, Tatiana A. Bubba, Tapio Helin, Luca Ratti
arXiv:2605. 17189v2 Announce Type: replace-cross Abstract: Inductive matrix completion (IMC) is a variant of low-rank matrix completion that incorporates row and column side-information.
By Yuepeng Yang, Cong Ma